{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from statsmodels.tsa.stattools import adfuller"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_ar_process(lags, coefs, length):\n",
    "    \n",
    "    #cast coefs to np array\n",
    "    coefs = np.array(coefs)\n",
    "    \n",
    "    #initial values\n",
    "    series = [np.random.normal() for _ in range(lags)]\n",
    "    \n",
    "    for _ in range(length):\n",
    "        #get previous values of the series, reversed\n",
    "        prev_vals = series[-lags:][::-1]\n",
    "        \n",
    "        #get new value of time series\n",
    "        new_val = np.sum(np.array(prev_vals) * coefs) + np.random.normal()\n",
    "        \n",
    "        series.append(new_val)\n",
    "        \n",
    "    return np.array(series)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def perform_adf_test(series):\n",
    "    result = adfuller(series)\n",
    "    print('ADF Statistic: %f' % result[0])\n",
    "    print('p-value: %f' % result[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# AR(1) Process"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Stationary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Stationary AR(1) Process')"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ar_1_process = generate_ar_process(1, [.5], 100)\n",
    "plt.figure(figsize=(10,4))\n",
    "plt.plot(ar_1_process)\n",
    "plt.title('Stationary AR(1) Process', fontsize=18)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ADF Statistic: -5.612850\n",
      "p-value: 0.000001\n"
     ]
    }
   ],
   "source": [
    "perform_adf_test(ar_1_process)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Non-Stationary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Non-Stationary AR(1) Process')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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W7k6M4K0K4/elGCOQnO/wO/iS/fXSipEvuBVjRFUN5LmSm9yGe5O99oQQo5ZS6j2MEgRJuu8ipx6hlLoTIyhL11oPqRSCMqrnHwbu1Fo7S4AXQniQ5EgJIUYle7mCczES770uiLL7G8YU10+GcY47MUYFH3RJj4QQLiUjUkKIUUUpdRpGPaJb7V+na60LPdopIcS4JSNSQojR5nsY+wCGA1dKECWE8CQZkRJCCCGEGCKPlD+IiYnRaWlpnri0EEIIIcSg7Nixo0ZrHevsPo8EUmlpaWzfvr3/hkIIIYQQHqaUOtrbfZIjJYQQQggxRBJICSGEEEIMkQRSQgghhBBDJIGUEEIIIcQQSSAlhBBCCDFEEkgJIYQQQgyRBFJCCCGEEEMkgZQQwitorXljVynFdS2e7ooQQgyYBFJCCK/w9OZCbntpN//10BaO1jZ7ujtCCDEgEkgJITzuq8I6fvduDoszomm3WLni0a2UHJORKSGE95NASgjhUVWNbXz/+Z1MjAri4asX8OwNp2Fu6+SKR7dS3tDq6e4JIUSfJJASQnhMp9XGLS/spKnNwkNXn0pEkB+zkiN45obTqGvu4MpHt1JlbvN0N4UQolcSSAkhPOb37+XwVeEx/nDZbLISwo8fn5sSyVPXL6SisY0rH91KbVO7B3sphBC9k0BKCOERb+4u5clNhVy/LI1L5ib3uH9BWjSPX7uQoroWfvXWfg/0UAgh+ieBlBBixBXXtXDna/tYlBbNXRdM77XdkskTuPH0DN7dW05OeeMI9lAIIQZGAikhxIi7550DKAV///Zc/Hz7/jN04+kZhAWY+Nsn+SPUOyGEGDgJpIQQI2p9XhUfHajkh6sySYwI6rd9RLAfN5yezof7K8kubRiBHgohxMBJICWEGDHtFiu/efsAGTEh3LA8fcCPW7s8nYggP/76sYxKCSG8iwRSQogR89gXRzhS08zdF8/E3zTwPz/hgX7ctCKDdblV7Co65sYeCiHE4LgkkFJK3a6U2q+UylZK/VspFeiK8wohxo6y+lb+ta6Ac2fGs2Jq7KAff93SNKJD/GVUSgjhVYYdSCmlkoFbgQVa61mAL/Ct4Z5XCDG23PteDjat+cWFM4b0+JAAE989I4MvDtbwVWGdi3snhBBD46qpPRMQpJQyAcFAmYvOK4QYAzYV1PDu3nJuOXMKKdHBQz7P1YvTiAkN4K8fnTwq1dDaydbDtVQ0SBV0IcTIMg33BFrrUqXUn4EioBX4SGv9kWM7pdRNwE0Aqampw72sEGKU6LTa+PVb+0mNDuamFRnDOleQvy/fXzmZ375zgN+8vZ/KxjaySxspqjM2OA4LMPGPb8/jzKw4V3RdCCH65YqpvSjgEiAdSAJClFJXObbTWj+itV6gtV4QGzv4/AghxOi07UgdBVVN/PTcaQT6+Q77fFeclkpyZBBPbioku7SRWcnh/PTcaTx89amkRAez9umveGjDIbTWLui9EEL0bdgjUsBq4IjWuhpAKfUfYCnwnAvOLYQY5TYW1GDyUaxy0ShRoJ8v7992OlpDRJDfSfednhnDT1/dyx/ezyW3vJE/XHaKS4I3IYTojSsCqSJgsVIqGGNq7yxguwvOK4QYAzYV1DA/NYqQAFf8uTGEB/o5PR7sb+Jf357HjMRw/vRhHodrmvnjZacwMSqI0AATSimX9UEIIcA1OVJblVKvAjsBC7ALeGS45xVCjH71LR3sK23gtrOmjtg1lVLccuYUpsaHcduLuzj/718A4G/yISbEn5iwAFZlxXHb6pHrkxBi7HLJR0St9a+BX7viXEKIsWPLoVq0huWZE0b82mfPiOeD21bwVWEdtU0d1DS3U2PuIKe8kb9/epDL5k8c1gpCIYQAFwVSQgjhzMaCGkIDTJwyMdIj10+JDu4RLJU3tLL8j5/x3JdH+fkF0z3SLyHE2CFbxAgh3GZTQQ2LM6Lx8/WePzWJEUGcOzOeF78qprXD6unuCCFGOe/56zaGvb2njANljZ7uhhAjqriuhcLaFpZNifF0V3q4dkkaDa2dvLWn1NNdEUKMchJIuVlbp5Ufv7ybKx77koKqJk93R4gRs/lQDQDLvTCQWpQeTVZCGE9tPir1poQQwyKBlJsdKG+k06oxt1m49oltVDXKFhZifNhYUEtcWABT4kI93ZUelFJcuzSNnPJGth895unuCCFGMQmk3GxPcT0AD191KsdaOrjuya8wt3V6uFeesavo2Lj93scbm02zuaCG5VNivLZ20yVzkwgPNPHU5kJPd0UIMYpJIOVmu4vrSQgPZPWMeB64cj75lWa+99xOOiw2T3dtxFhtmvvez+HSBzbzyzeyPd0dMQJyK8zUNnd4ZX5Ul2B/E99cmMIH2RWy2bEQYsgkkHKzPcX1zEmJAGDltDj+cNkpbCyo4Wev7sFmG/u5GU3tFm5+djsPbzhMSnQQb+8tp7S+1dPdEm62qcDIj/LmQArg6sVp2LTmha1HPd0VIcQoJYGUG9W3dFBY28KclBM1dL5x6kR+eu403thdxv2fFbj1+rVN7R7NySqua+EbD27ms7xqfnvJTF68aQkAT2w84rE+iZGxsaCGKXGhJEQEerorfUqdEMyqaXG8sK2IdouUQhBCDJ4U5HSj3fb8qLkpJxcj/P7KyeSUN/Kvzwq47NSJJEUGDftaNU3trMupIrfCTF5lI3kVTdQ0tRMaYGL7L1aP+MatXxXW8d1nd9BptfHU9Qs5PTMWgK+dksiL24q49azMHhvOirGh3WJl25E6vrkwxdNdGZBrlqZx7RPbeH9fBefPTqCwpoX8SjMHK82EB/mxdlk6Pj7emeclhPA8CaTcaE9xA0rB7OSIk44rpbjz/Cw+OlDJXz7K5y+XzxnyNbTW/GdnKb995wANrZ0E+fkyNT6UM6fFYtPw2s4S8irMJ42KuduOo3Vc+dhWkiODePzaBWTEnli1ddOKybyxu4zntx7l+yunjFifxMjZVVRPa6fV66f1upw+JYaMmBB+/p99/Pcre7Dap9yVAq2hsc3Cj8+WffmEEM5JIOVGu4uPkRkXSpiTneonRgVz/bI0Hvn8MGuXpzEzKaJHG5tN85NX9nCgvJHL5k9kzbxkYsMCjt9fWt/KXf/Zx4b8ahZMiuLui2cyIzH8+KfnotoWXttZwv6yxhELpIrrWrjpmR0kRQTy2veWEh3if9L9M5LCOT0zhic3FXLD8nQCTCM7Uibcb1NBDb4+itMyoj3dlQHx8VH84qLpvLqjhIyYUDLjQ8mMCyMjNoRfvpHNPz49yPSEMM6fnejprgohvJAEUm6itWZPSQNnZcX12ub7K6fw8lfF3PdeLs/esKjHMvF/fVbAf3aVkhEbwr3v5fDHD3JZlRXHfy1IoaKhlT+8n4sGfnPxTK5ePKnH9ENKdBBhgSb2lzW441vswdzWyXee3k6n1cbj1y3sEUR1uWlFBlc/vo03d5Vx+SiZ/hEDt7GghjkTIwh38gHCW63KimdVVnyP47+7dBYF1U389yt7SIsJYXpiuAd6J4TwZpJs7iYlx1qpa+7ocyQoIsiPH67KZGNBDRvyq0+675MDlfz143wunZfMpz8+g09+vIIblqezs6ieG5/Zzi/f3M/8SVF8eNsKrl2a5jSHQynFjMRwskdgexqrTXPrv3dRUN3EA1eeyuTY3oswLp8Sw/TEcB754vC4WLk4njS0drKnuN4rq5kPRYDJl4euOpXQABM3PbudY80dnu6SEMLLSCDlJrt6STR3dNXiSUyaEMx97+Uez80oqGri9pd2Mzs5gvu+PhulFFPiwvj5BdPZ8vNVPHbNAh69ZgHPrF3UY2d7R7OSI8gtb8RidW/dqnvfzeGzvGp+c/FMlmf2/SaqlOKmFekUVDWxPr/Krf0SI8ditXHna3uxaTizj5HY0SY+PJCHrz6VyoZ2bnlhp9t/l4QQo4sEUm6yp7ieAJMP0xLC+mznb/LhjvOyyKs08+qOYhrbOrnp2e34m3x4+OpTe6y28/P1YfWMeM6eET+gitEzk8Jpt9g4XNM8rO+nLy9sLeKJTUe4bmkaVy2eNKDHXHRKEkkRgTy84bDb+iVGjs2mueO1fbyfXcEvLpzOvNQoT3fJpealRvH7r89m86Fa7n0vx+3XO1TdRKcEbEKMChJIucnu4npmJUfg59v/U3z+rATmp0byl4/y+dG/d1FU28IDV853SVmEriT27FL35ElVmdv41ZvZnDE1ll9cOH3Aj/Pz9WHt8nS2Hqk7vo2OGJ201tz99n5e21nC7aun8p3TMzzdJbf4xqkTuWbJJJ7cVEhRbYvbrnOw0szZf93AU5sK3XYNIYTrSCDlBp1WG9mlDf1O63VRSvE/F06nytzOZ3nV/PprMzgtY4JL+jI5NoQAkw/73ZQnta+kAYtNc+tZUzANIGjs7luLUgnx9+Xl7cVu6ZsYGX/6MI9nthzlphUZ3HrW2C5psXZZOgDrcivddo3HvjiCTcNHByrcdg0hhOtIIOUGeRVm2i22QZUcOHVSNDefkcEPzpwy4OmxgTD5+pCVGO62lXs55UaANi1h8KuZQgNMzEyKIL/S7OpuiRFy/2cFPLD+EFeelsrPz8/y2g2KXSUtJoSM2BDW5VX333gIqs3tvL6rlGB/X3YcPSbJ7UKMAhJIuUFXRfN5g6zd9PPzp/OTc6e5/M1oZlI4+8sa0dr1K+Ryys2kRgcTGjC0ShpT4kPJr2xyS9+Ee20uqOFPH+Zx6bxk7rlk1pgPorqclRXHl4dqaW63uPzcz24ppNNm43drZmHT8PlB9wRsQgjXkUDKDfYU1xMd4s/EqOHnOLnCrKQIzG0Wiutcv1lwTkUj0xP7TqjvS2ZcKA2tnVQ3tbuwV2IkvLOvnBB/X+77+uxxtYXKqqx4Oqw2Nto3ZnaVtk4rz355lLOy4lkzN5kJIf58miOrWoXwdhJIucHu4nrmTIzwmk/oM5OMaTdXT++1dlgprGkmawjTel0y44wgrKCyyVXdEiNAa82nOZWsmBo74vs4etqCtCjCAk2sc3GQ89rOEo61dPKd0429/VZOi2NDfrWUWxDCy0kg5WLmtk4KqpuYm+I9y7+nJYTh66PIdnEglVdpxqYZVrXnzHijcOfBKgmkRpPs0kYqG9tZPb1nNfCxzs/XhxVTY1mXV+WygrI2m+bxL44wOzmC09KNrXXOmh5HQ2snO4tkVasQ3swlgZRSKlIp9apSKlcplaOUWuKK845G+0ob0BrmpPTcO89TAv18yYwLdfnKva5E8xnDCKTiwgIICzRxsEoSzkeTj3Mq8VFjq/DmYJyVFUe1ud1lH07W5VZxuKaZ75yefnwke3lmDCYfxaduXCEohBg+V41I/R34QGudBcwB3F+xzkvtHmBF85E2w55w7kq55Y2EBpiGlQumlCIzLpSDMrU3qnyaU8mpk6J63U9xrFs5LQ6lcFkO06NfHCYpIpALum2MHB7ox6L0aD7LlTwpIbzZsAMppVQ4sAJ4HEBr3aG1Hrdj0XuK60mbEExksHe9wcxMiqDa3E5VY5vLzplTbmZaQtiwE40z48IokKm9UaOsvpX9ZY3jclqvS3SIP/NTo1jngiBnX0kDW4/Ucf2y9B4FfFdlxZFf2URxnfsKgAohhscVI1IZQDXwpFJql1LqMaVUiGMjpdRNSqntSqnt1dVjc0lvu8XKrqL6QdWPGimzjiecu2ZUSms97BV7XTLjQ6lt7qBWVu6NCp/mGFNNZ43jQAqMIGdfacOwP5w8tvEwoQEmvrkoxek1AD7Lk1EpIbyVKwIpEzAfeFBrPQ9oBu50bKS1fkRrvUBrvSA2NtYFl/Uu7RYrtzy/kypz+0nD895ihotX7pUca8XcZhlWonmXKXFGwrmMSo0On+RUkR4TwuTYHp+XxhVXBDlbDtXyzt5yvrkwhfBAvx73Z8SGkh4TImUQhPBirgikSoASrfVW+/9fxQisxo2uIOqTnCruuWQm585M8HSXeggL9GPShGCyS10zIpVbYSSHD6f0QZfMeGNUS1bueb+mdgtbDtVyVlac15T38JSshDCSIgKHHOR8cqCSa5/cRkZMCN9bObnXdquy4thyuJaWDtcXABVCDN+wAymtdQVQrJSaZj90FnBguKFbTFAAACAASURBVOcdLdotVr7/nD2IWjOLq5ekebpLvZqVFMH+cteMSOWUN6KU8WYyXEkRgYT4+8qI1Ciw8WA1HVYbq2eM72k9MBZKrJoex8aCGto6rYN67Ou7Srj5uR1MTwjj5ZuXEBMa0GvbVVlxdFhsbCqoHW6XhRBu4KpVez8EnldK7QXmAr930Xm9WlcQ9WluFb9bM4urXbhHnjvMSAqnuK6VhpbOHvcNdouWnPJGJkUHEzLErWG6U0oxJS5USiCMAh8fqCIiyI8Fk7ynTponnZUVT0uHla1H6gb8mKc3F3L7S3tYlBbN8zcuJqqflY8L06IJDTC5daNkIcTQuSSQ0lrvtuc/naK1XqO1PuaK83ozm01zy/MngihXbjTsLscrnHcblbLZNH/9OJ9Fv/+UgkEEMjnljS7Jj+oyJS5MSiB4OatN81leFWdOi8XkK7V8AZZMnkCgnw/rcvoPcrTW/OPTg/z6rf2cPSOeJ69fOKA9Kv1NPqyYGsO63CrZk1IILyR/DYdofX4Vn+RU8T8XTB8VQRQYJRAADthX7jW1W/juczv4x6cHqWvu4J53Blb+q7ndwtG6FpfkR3XJjA+lytzudLRMeIddRceoa+6Qab1uAv18WTY5hk8HEORsPVLHXz/O5+vzknnwyvmD2lrnzGlxVDa2u7wWnBBi+CSQGqInNxUSHx7AdcvSPN2VAYsNCyA+PID9ZY0U17Vw2QOb+SSnkl9dNIOfn5/FhvzqARX/y6s0ozUuKX3QJbNr5V61TO95q49zKjH5KFZMHXurbodj1fQ4So61klPe92v3rT1lBPn5cu+lswc9otdVQX69lEEQwutIIDUEByvNfHGwhqsXT+pRQM/bzUyK4IuDNVz8r41UNLbx9NpFrF2ezjVL0siICeGedw/Q2c8mqV1bw7hyam9q18o9md7zWp/mVLE4Y4LTZfrj2XkzEzD5KN7cXdprG4vVxofZFayaHkeQ/+A3eY4JDSAzLpQdR8d81oQQo87oigK8xJObC/E3+fDtRame7sqgzUoKp6apnQmhAbx5yzJOzzRGF/xNPvzPhdM5XN3Ms1uO9nmOnPJGwoa5NYyj5MggAv18pASClyqsaaagqomzpo/PvfX6MiE0gBVTY3lrT1mvmxhvPVJHbXMHFw2jxtz81Ch2FddLnpQQXkYCqUGqb+ngPztLWDM3iQl9LFn2VlecNonbV0/l9e8vJS3m5IKKq7LiOD0zhr99kk9dc0ev58gpN5OVGObSOkI+Pl0r9ySQ8kZfHDR2I1g1Tjcp7s+aecmUN7T1unrv3X3lBPn5snLa0J+/+ZMiqW/p5HBN85DPIYRwPQmkBunFr4pp67Rx/bJ0T3dlSBIiAvnR6kzCnEzPKKX41UUzaO6w8n8f5zt9vM2myaswu3Rar0tmXBgFlZIj5Y32ljQQHeJPanSwp7vilc6eHk+Ivy9v7Oo5vdc1rXfWEKf1usxPNUpO7JTpPSG8igRSg2Cx2nh2y1EWZ0S7JZDwBpnxYVx1WirPbz1KXkXPoKbkWCtN7a7ZGsbRlLhQyhraMLfJyj1vs6+0gVnJEeO+mnlvgvx9OXdmAu9ll/coztk1rXfhMLeOmhwbSnigiZ1F43ZPeCG8kgRSg/DxgUpK61tH7WjUQN22eiphgX7c886BHvkYB+yJ5q6oaO6oa+XeoWqZuvAmbZ1WDlY1MTt5bH54cJU185Ixt1l6rKxzxbQeGNPfc1Oj2FUkI1JCeBMJpJw4UtOMxcnKtSc3FTIxKojVY3zX+6gQf25fncnGghruen3fSZ+wu7aGmeaOQOr4yj2Z3vMmOeWNWG2a2ckRnu6KV1s6eQIxoQG83m16z2K18YELpvW6zE+NJK/SLKO2QngRCaQcHChr5Mw/r2fVXzbw7JdHjwcR2aUNbCus49olafj6jP3pjWuWpPG9lZP597Zivv7AZo7WGqNEuRWNpE8IIdh/+FvDOEqJCsLfJCv3vE22vQjkLAmk+mTy9eHiOUl8llt9vLDs1iN11LlgWq/L/NQotIbdxTK9J4S3kEDKQUG18Sbu56v45RvZLP/jOv617iAPrj9EsL8vly9M8XAPR4aPj+KO87J4/NoFlNa3ctE/N/JBdsXxFXvuYPL1ISMmREakvEx2SQNRwX4kR7qu3MVYtWZeEh1WG+9llwPwzt5ygv2HP63XZW5qJErBzqMSSAnhLSSQclBW3wrAG7cs48WbFjMzKYI/f5TPu/vKuWz+RCKCxlcxwrOmx/POD5eTHhPCd5/bQVFdC9NduDWMo8z4MBmR8jKSaD5ws5MjyIgN4Y1dpcZqvf0VrMpyzbQeQHigH5lxoeyUPCkhvIYEUg7K6lsJDzQRFujH4owJPL12Ee/dejrfWzmZH66a4unueURKdDCvfHcJ1ywx9hRcmB7ttmtlxoVScqyVlg5Lv23X5VbyyYH+N4sVQ9fWaSW/0iz5UQOklGLN3GS2HqnjP7tKqWvu4KJTXDOt12W+PeG8t+KfQoiRJYGUg7L6VpIcpjBmJIVzx3lZxIUHeqhXnhdg8uW3l8xi96/OZnHGBLdd5/jKvareV+61dVq56/V9rH1qO99/YSclx1rc1p/xLq/CjEUSzQdlzdxkAO55+4BLp/W6zE+NorHNwuEaGbkVwhtIIOWgtL5NckH6EBns79bzZ8YbgdTBKud5UgVVZtbcv4kXthZx9eJJKOBPH+a5tU/j2b7SBkASzQcjdUIw81MjMbdbWJUVR6Cfa6b1usyfFAlInpQQ3kICKQfORqTEyJk0IQSTj+Lz/GqySxuoaWrHZtNorXl5ezFf++cmqs3tPHX9Qu5ZM4sbT8/gzd1l7JFVTG6RXdpARJCfS/dVHA8unWeMSrlqtV53GTFdhTklT0oIb+D6NeyjWFO7hYbWTgmkPMjP14eZyRG8sbuMN3aX2Y8pokP8qWxsZ0nGBP72rbnE26dZv7tyMi9+VcS97+bw0s2LJSHaxfaVNjBbEs0H7fKFKYQF+nHOzASXn9vHRzEvNUoCKSG8hARS3XSt2EuKHL+5UN7ghe+cxsGqJioa2qhoaKWisZ2KhlZmJUdw/bL0k+p4hQaYuP3sqfzP69l8dKCSc93wxjVetVuMRPMblmd4uiujToDJlzX2USl3mJ8axd8+raaxrZNwJ/tmCiFGjgRS3ZTaAynJkfKskAATc1MiYYAlu765IIWnNhXyh/dzOXNaHP4mmbF2hbwKM51WSTT3RvMnRRqFOYvqWTE11tPdEWJck3ecbrpGpJIlH2RUMfn6cNcF0zlS08wLW496ujtjRleiuQRS3mduir0wp0zvCeFxEkh1U1bfiq+PIi5MpvZGm5XTYlk+JYa/f3qQhlbZh8wVsksbiQjyIyVaPlh4m7BAP6bGhbGzSBZZCOFpEkh1U1bfRkJ44LjYS2+sUUpx1wXTqW/t5P7PCvpt32GxUVjTe60qYazYm5UcLonmXmr+pEgpzCmEF5BAqpvS+lbJjxrFZiSF8/V5E3l6cyF1zR19tv3zR3mc83+fU21uH6HejS4dFht5FWapH+XF5qVGYW6zcMi+P2i7xcqOo3U8+vlh9pU0eLh3QowfLks2V0r5AtuBUq31Ra4670gqq29lwaQoT3dDDMPNZ2Tw2s4S/r2tiFvOdL6lj7mtkxe2FtFhtfFBdjlXL0kb2U6OAvmVZjqsNsmP8mLzU42/Vfe9n0tTu4U9xfW0W2wALEqL5uXvLvFk94QYN1w5IvUjIMeF5xtRVpumoqFNakiNclPjwzg9M4ZnthTSabU5bfPSV8U0tVuIDvHn7T3lI9vBUUISzb1fRkwIiRGBbMivpq3TylWLJ/HQVady7ZJJ7Cg6RmOb5AoKMRJcMiKllJoIXAjcC/zYFeccadXmdiw2LYHUGHD9sjTWPrWd9/aVc8nck2v5WKw2ntpcyKK0aJZnxvB/n+RT3tBKYoT83LvbV9pAeKCJ1OhgT3dF9MLHR/HBbSvw9VGEBpz4Ux4d4s/TW46yuaCG82a5vrK6EOJkrhqR+hvwM8D5EACglLpJKbVdKbW9urraRZd1HakhNXasnBpHekwIT24q7HHfRwcqKTnWytrl6Vx0SiJaw7t7ZVTKkZFoLhXNvV1EkN9JQRTAvNRIwgJMrM/zvr+zQoxFww6klFIXAVVa6x19tdNaP6K1XqC1XhAb630F5E5UNZdAarTz8VFcvyyN3cX1PersPL7xCKnRwZw9I56M2FBmJoXzjgRSJ+mw2MgtN8u03ijl5+vD8swYNuRXo7Ws6BPC3VwxIrUMuFgpVQi8CKxSSj3ngvOOKNkeZmy5bP5EwgJNPLHxyPFjO4uOsePoMa5flna8xMXX5iSxu7ie4roWT3XV63Qlms+UQGrUOmNqLOUNbeRXNnm6K0KMecMOpLTWP9daT9RapwHfAtZpra8ads9GWFl9K2GBJsJk36oxISTAxLcWpvB+dsXxIPnxjUcICzTxXwtO7D1z4Wwjh0RGpU7YXyaJ5qPdGdOMUf8N+VUe7okQY5/UkbIrrW+T/Kgx5polaWiteWbLUUqOtfBBdgVXLEo9KackJTqYeamRvL2nzIM99S4HyhoJ8fdlkiSaj1qJEUFMiw9jQ77kSQnhbi4NpLTW60dzDSkJpMaWlOhgzp2ZwL+3FfHQhkMAXLs0rUe7i05J4kB54/HChuNdboWZaQlh+EiF/1Ft5bRYvjpyjOZ2i6e7IsSYJiNSdmUNrZJoPgatXZ5OQ2snz31ZxAWzE53+jC+cnYhS8I7UlEJrTW6FmazEcE93RQzTGVNj6bDa2HKo1tNdEWJMk0AKaG63UN/SKYHUGLRgUhSzko2g4Ibl6U7bJEQEsjAtmrf3lo37VU4VjW00tHYyPSHM010Rw7QgLZpgf1/WS56UEG4lgRRQ3iAr9sYqpRS/uXgmPz13GnNTIntt97VTEimoaiKv0jyCvfM+ueXG9y8jUqOfv8mHpZNjWJ8nZRCEcCcJpDASzUGKcY5Vp06K7nXfvS7nz07ER6b3yKloBGCajEiNCWdMi6XkWCuHa5o93RUhxiwJpIDSY1KMc7yLCQ1g6eSYcT+9l1dhJjkyiHApAzImrJxqL4MgVc6FcBsJpDBW7Pn6KOLCAjzdFeFBF89N4mhty5hIzn1+61G+9cgW7nh1Lw+sL+D9feUcKGukrdPa5+Nyy81kyWjUmJESHUxGbAjrpQyCEG7jkk2LR7uy+lYSwgMx+UpcOZ5dPCeJP32YxwPrD7F0SoynuzNkFquN//v4IKApqGqmpqn9+H2ZcaF8dPsKp3votVusHKpuYvWMuBHsrXC3lVPjeH7rUdo6rQT6+Xq6O0KMORI5YGxYLInmItDPlxuWp7OxoIa9JfWe7s6QbTlcS01TO79bM4vtv1hN9m/O5Z0fLuf6ZWkcrGqiqJftcA5VNWOxabISJNF8LDljWiztFhtbDo/+kVYhvJEEUkgNKXHClaelEh5o4oHPDnm6K0P2xq4ywgJNrJxmjCyFBpiYlRzBVYsnAbCpwPkbaq490Xx6okztjSWnpUcT6OfD+lwpgyCEO4z7QMpq01Q0tEkgJQAIC/TjmiVpfHiggoKq0VfpvK3Tyof7Kzh/VkKPaZyMmBASwgPZfKjG6WNzK8z4m3xImxAyEl0VIyTQz5fV0+N5aXuxbM4thBuM+0CqpqmdTquW0gfiuOuXpRFg8uHhDaNvVOqTnEqa2i2smZvc4z6lFEsnT2DLoVqnKxNzK8xkxoVKruAYdNcF0/FVil+8kT2uV6UK4Q7j/i9mab1R+kACKdFlQmgA31yQwuu7Simzvz5Gizd3lxEfHsBpGROc3r9k8gRqmzucFh7NLW+U/KgxKikyiP8+Zxob8qt5Z+/4rpUmhKuN+0Cq641SpvZEdzeuyADg0S8Oe7gnA1ff0sH6vCq+dkoSvr1sONy1GnGzQ55UbVM7VeZ2yY8aw65dmsbs5Ah+8/YBGlo6Pd0dIcYMCaTqZXsY0dPEqGAunpvEi9uKqWvu8HR3BuS9fRV0WjVr5vWc1uuSHBlE2oRgNjvUysqrsG8NIyNSY5avj+K+r8+mrrmdP3yQ2+P+5nYL972Xw58+7HmfEKJ3EkjVtxEWaCJMKjkLB987YzKtnVae2lzo6a4MyBu7S5kcG8LMpL6DoSWTY9h6uBaL1Xb8WE5XICUjUmParOQI1i5L59/biviqsO748c/zqznn/z7n4c8P88jnh/st3CqEOGHcB1Kl9a2SHyWcyowP45wZ8Ty9udDrR6VK61vZdqSONXOTnRbb7G7p5AmY2y1klzUeP5Zb3khMaAAxoVLdf6y7/eypJEcGcdd/9lFlbuPHL+/mmie2EeDnw3fPmEynVXOgvLH/EwkhAAmkKKuXGlKidz9anUlbp5VrnthKQ6v35pW8vacMMLa56c+SyUYievcyCHmVsjXMeBESYOKeNTM5WNXE8j98xlu7y/jBmVN479bTuW5pGgC7i0ZvQVohRpoEUlLVXPRhZlIED111KnkVZq5/chvN7RZPd8mpN3aVMi81kkkDqAEVExpAVkLY8YRzq02TVyGB1HiyKiueby9KZU5KBG/9YDk/OXcagX6+JEQEkhAeyO5iCaSEGKhxHUi1dFg41tIpI1KiT2dmxfGPb81jd3E933l6u9flj+RVmMmtMDutHdWbJZMn8FVhHe0WK4W1zbRbbGQlSqL5eHLf12fzyneXMsMhp25uSqQEUkIMwrgOpMrq2wCpISX6d/7sRP5y+Ry+PFLL957bQYfF1v+DRsgbu0vx9VFceErigB+zdHIM7RYbu4rqyS3vWrEnI1IC5qZGUlTXQm23za6FEL0b14FUUV0zIDWkxMBcOm8i966ZzWd51fzoxV20Wzw/MtVusfLqjhJWZMYMKlH8tIxofBRsLqght6IRXx/FlLhQN/ZUjBZzUyIB2DOKN+4WYiSN60Bqc0Et/iYfZiVFeLorYpS44rRUfnnRDN7PruD8v3/Bl4edbwA8Ut7ZU061uZ3rlqUP6nHhgX7MnhjJ5kO15FaYyYgJ6bE3nxifZidH4KMk4VyIgRrXgdT6/GpOS48myF/eQMTA3bA8nafXLqLTauNbj3zJz17dQ33LyJdH0FrzxKYjZMaFsiIzZtCPXzp5AruL69ldXM80mdYTdiEBJqbGh7FL8qSEGJBxG0iVHGuhoKqJM6bGerorYhQ6Y2osH912BjefkcFrO0s56y8beH1XyUlFLt1t65E69pc1snZ5er+1o5xZOnkCFpum2tzOdEk0F93MS41kT3E9NptscCxEf4YdSCmlUpRSnymlcpRS+5VSP3JFx9zt83yjhs7KaXEe7okYrYL8ffn5+dN5+wfLmRgdzO0v7WHObz7iuie38dCGQ+wprndrYPX4xiNEBftxaR9bwvRlwaRo/H2NPwGSaC66m5sSSWObhSO1zQN+zMFKM796M3tEP0wI4Q1cMSJlAf5baz0dWAzcopSa4YLzutX6vCqSI4OYHNt/3R0h+jIjKZz/fG8pD111Kl+fP5GSY6384f1cLrl/E/Pu+fikrThcpbCmmU9yKrnytElDzm0K8vdlXqqRWCylD0R3c1OigMHlST24/hDPbDnKwaomd3VLCK9kGu4JtNblQLn932alVA6QDBwY7rndpcNiY/OhWi6emzSkKREhHPn6KM6blcB5sxIAqDK3sfVwHT99dQ/v7StnYVq0S6/31OZCTD6Ka5ZMGtZ51sxLprXTSlKEFKUVJ0yJCyXE35fdxfVcdurEftu3dlj5cH8FALkVjTJVLMYVl+ZIKaXSgHnAVif33aSU2q6U2l5dXe3Kyw7ajqPHaGq3sFLyo4SbxIUF8rU5ScxLiXL5iFRjWyevbC/ma6ckERc+vADo24tSeesHy+UDhTiJr4/ilIkDL8z5SU4lzR1GOZAce10yIcYLlwVSSqlQ4DXgNq11jx0vtdaPaK0XaK0XxMZ6NoDZkF+NyUexdMrgVzoJMRgL06I4UNaIuc11+/S9tK2Y5g4ra5cPruSBEIMxNzWSnPLGAVXyf3N3KQnhgUxPDCdHNjwW44xLAimllB9GEPW81vo/rjinO23Ir2ZBWhShAcOe2RSiTwvTo7Fp2OWimjwWq42nNheyKD2aWclS/0y4z9yUSCw2zf6yhj7bHWvuYH1eNRfPTWJmUji5FTIiJcYXV6zaU8DjQI7W+q/D75J7VTa2kVPeKKv1xIiYlxqFr48a0vTeY18c5uf/2ctDGw7xQXY5OeWNvLm7jNL6Vm6Q0SjhZvPsFc77+xDwXnY5Fpvm4jlJZCWEUW1up0a2lxHjiCuGZJYBVwP7lFK77cfu0lq/54Jzu9yGfCM/S+pHiZEQGmBiRmI4244MLpCy2jR/+jAPm9Z0Wk+u5ZMaHczq6fGu7KYQPcSFB5IUEdhvntSbu8qYEhfKzKRwGluNKezccjPLMwe+ZZEQo5krVu1tBEZNpuqG/GriwwOkbo4YMQvTonl+61E6LDb8TQMbBC6qa6HdYuN/v3EK581KoKi2hcLaZo7WtrA4YwK+PqPmV06MYnNT+044L61vZVthHT85ZypKqeMV8nPKG1k+hGr7QoxG46qyucVq44v8as6YGiurlMSIWZQeRbvFxr7SvnNNusuvNPJMpsaHER7ox6zkCC46JYlbzpzCqZOi3NVVIU4yNyWSkmOtvU7VvbW7DICL5xhFYSeEBhAXFkBOhSScd7flUC3n/e1zjjWP/FZSwv3GVSC1p6SexjYLZ0yV/Cgxck6dZNSQGkyeVIG9qGFmXKhb+iTEQPRXmPPN3aXMT40kdULw8WPTE8PJHeESCPtKGmhodd3KWFfbctjYHPyl7cWe7opwg3EVSK3Pq8ZHwXIpeyBGUGxYABkxIWwfRCCVX2kmOTKIEFlZKjxodnIEvj7K6fRebkUjuRVm1jhsUZSVGEZBVROdI7RVTENrJ5c9uJn//SB3RK43FCV1LQA8v/UoVtm/cMwZV4HUhvxq5qdGERHs5+muiHFmYVo0XxUeG/AmsPmVTUyNl9Eo4VlB/r5Miw9zGki9ubsMXx/FBbMTTzo+IzGcDquNw9UD36dvOD7Pr6bDauP97Aqv3eevqK4Ff5MPxXWtbMiv8nR3hIuNm0CqpqmdvSUNslpPeMSCtCgaWjsHtA+Z1aY5VN1EZrwsiBCetyg9mo0FNVxy/yae2nSEmqZ2bDbNW7vLOD0zhpjQk1fnZSUY28PkjlCe1LpcIzCpa+7gy8Ou39fSFYqPtXDBrATiwwN4ZstRT3dHuNi4CaQ2H6oFYIUEUsIDFqUPPE/qaG0zHRab5EcJr/DTc6fx8/Oz6LDYuPvtA5z2+0/5r4e3UFrfypq5yT3aZ8SG4O/rw4ERqHButWnW51Vx4exEQvx9eXdfmduvOVhtnVYqG9tJjwnl24tS2ZBfzdHakRmtEyNj3ARS+0rq8Tf5MCNJNtMUIy81Opi4sIABBVL5lcao1VQZkRJeICTAxM1nTOb9H53Oh7et4KYVGVQ0tBEd4s/ZM3rWM/Pz9WFKXOiIJJzvLj7GsZZOLpidyOoZ8XyQXTFiuVkDVXKsFYDUCUFcsSgVX6V47ksZlRpLxk0gtb+skekJYfj5jptvWXgRpRQL06P5agCFOQ/aSx9MkREp4WWmJYRxx3lZfPGzM9l856peF0NkJYaNyJ57n+ZUYfJRnD41hgtnJ3KspZMt9tkHb1F8zEg0T4kKJi48kHNnJfDy9hJaO/rfw1CMDuMiqtBak13awIwk2ZtMeM7CSVGUNbRRYv/D2pv8qiYmRsmKPeG9fHwUgX6+vd4/IzGcKnM7tW7eKmZdbhUL06IJD/RjxdRYQgNMvLu33K3XHKxi+4q91GijRMQ1iyfR0NrJ23u8bxpSDM24CKRKjrXS2GZhpkzrCQ9aaM+T2l54rM92ByvNMq0nRrWuhPM8N25gXFrfSm6FmbOmG3UBA/18OXtGPB/s967pveK6FgJMPsSGGUn5i9KjmRYfxjNfFqK1lEIYC8ZFILW/zBhilkBKeFJWQjhhASa29ZEnZbEvG5dEczGaTU80Pgi4M+G8a7XemVknCixfODuRhtZONhXUuO26g1VU18LEqKDju2kopbh6ySSySxvZ1c8+hmJ0GBeB1IGyBnzUiU9JQniCr49i/qSoPvOkjta10GG1SekDMapNCA0gNiyAXDeOSK3LqSRtQjAZMSHHj50+NYawQO+a3iuuaz0+rdfl0nnJhAWYeFZKIYwJ4yKQyi5rZEpcKEH+vc/pCzESFqVHc7Cqqdc9tw4e32NPRqTE6DY9MdxtCeetHVY2H6plVVb8SfumBph8OWdGAh/ur6DD4vnpPa01xXUtpDgEUiEBJi47dSLv7i2X/ffGgHERSO0va2CmJJoLL7AwzZ4nddR5nlRX6QNZsSdGu+kJYRysbHJLtfHNh2pot9hYldVz39SLTkmksc3CxoJql193sBpaOzG3W3qMSAFceEoiHVYbO4v6zpkU3m/MB1I1Te1UNrZLfpTwCqdMjCDIz5d1uZVO78+vNJMSHUSwv6zYE6NbVmIYHVYbR2pcX3zy09wqQvx9jxe67W7ZlBjCA0284wXTe0X2FXsTo3oGUjMSw1EKsktHpgK8cJ8xH0h1JZpLIU7hDQL9fDl3Zjzv7i2n3dKzjszByiamxkl+lBj9picaf3OHmnButWke++Jwj5V/Wms+y61ixdRY/E0938L8TT6cOzOBj/dXOv0dG0nFdfZinE5GpEICTKTHhJBd1jDS3RIuNuYDqexS40U6M1Gm9oR3uHT+RBrbLHyWe/LUQ6fVxuGaJqZIfpQYAzJiQvHzVUNOON9eWMfv3s3hon9+wb/WHTw+RZhTbqa8oe2k1XqOLjwlEXO7hS/yPbt673gxzuggp/fPSopgf6kEUqPdmA+kDpQ1khIdRESwn6e7IgQAyyZPICY0gDd2lZ50/GhtM51WLSNSYkzwhMEqIgAAGq5JREFUN/kwJW7oFc43HarFR8Hq6fH8+aN8Ln1gM3kV5uPT4mdO6z2Q6pre+yTH+RT6SCmqayEq2I+wQOfvP7OSwylraKNOEs5HtTEfSO0va5DRKOFVTL4+XDwniXW5VTS0dh4/flD22BNjzPSEsCHvubepoIbZEyN58KpTefDK+ZTVt3LRP7/gqc2FzEmJPF7g0hk/Xx/mT4pit4frNDlbsdfdLPsiqP0yvTeqjelAytzWSWFtiySaC69z6bxkOqw23t93IiE2v7IJpWTFnhg7pieGU9HYNuitYpraLewprmfZ5AkAnD87kY9uX8E5MxOoaergHCebJTuaMzGS/Eozze2WIfXdFfoLpLpWk0vC+eg2pgOpA10VzZMlkBLeZVZyOJNjQ3i92/RefpWZlKhgqXcmxowl9kDozd2D21du25FaLDbN8ikxx49NCA3g/ivm896tp3PTiox+zzE3JRKbPpEnO9KsNk1pfSspTlbsdYkI9mNiVJAknI9yYzqQOrE1jEztCe+ilOLSeclsPVJHab2xssfYY09Go8TYMSs5goVpUTy1uRCrbeD7ym08WEuAyZieczQjKRw/3/7fuk6ZaPzd31Pimem9isY2Oq3a6Yq97iThfPQb84FUTGgAcX3MpQvhKZfMTQbgzd2ldNrr7UyRRHMxxqxdlk5RXQufDiLxe/OhGhamRRPoN/TR2QmhAaREB7Gn2DNBSnFd3yv2usxKDqewtgVzW2ef7YT3ckkgpZQ6TymVp5QqUErd6YpzuoJR0Tz8pC0EhPAWKdHBLEyL4vWdpRTW2FfsyYiUGGPOnhFPcmQQT2w6MqD21eZ2civMLJ0yYdjXnjMx0mMJ513FOPsbkZqZbIycdaWijIQ/vJ/rVfsRjnbDDqSUUr7A/cD5wAzg20qpGcM973C1dVopqGqSRHPh1dbMS+ZgVRNv7DZypWTFnhhrTL4+XLt0El8erhvQ6rTNh4zaT8smx/TTsn9zUyIprW+l2jy4ZHdXKKlrwUdBUmQ/I1JdCed9BFLbjtQNamq0L1ab5omNR3hhm2yY7CquGJFaBBRorQ9rrTuAF4FLXHDeYcmvNGOxacmPEl7twtmJ+PkqnthYiFIwOVZGpMTY880FqQT7+/LkpsJ+224uqCU80MSs5OH/7Z6TEgnAHg+MShXVtZAYEdRvPldsmJF+0lue1KaCGi5/eAvPb3VN4FNW30qH1cbekgZsLgrOxjtXBFLJQHG3/5fYj51EKXWTUmq7Ump7dbX7N5M8kWguI1LCe0UG+3PmtDhaO62kRsuKPTE2RQT78Y1TJ/LW7rI+R4e01mwsqGHJ5An4+gw/JWNWUgS+PsojCefFx1r7zY/qMis5oteVe69sN95en91yFK2HH/gctu99aG6zcNQ+/SiGxxWBlLNXe4+fttb6Ea31Aq31gtjYWBdctm/7yxoIDTD1Oz8thKddOs/43JEpieZiDLtuaRodVlufIytFdS2U1reybMrwp/UAgvx9mRYf5pE8qeK6lj5LH3Q3KymcgqomWjtO3hvQ3NbJB/srSIoI5GBVE1uP1A27X0eqm47/e6+HVjSONa4IpEqAlG7/nwgMrmiIG+wva2RGUjg+LvhUI4Q7nZkVR0J4IAvSei71FmKsyIgNZVVWHM99ebTXzYQ3FdQCuCyQAmN6b09xvUtGcwaqrdNKlbl9wB/kZyZHYNOQW3FyntR7+8pp67Txl8vnEhHkx7NfDn9670hNM6EBJgJMPuwrkbILruCKQOorIFMpla6U8ge+BbzlgvMOmdWmySlvlGk9MSoE+vmy4WcruXkARQaFGM3WLkunpqmDt/c4XzG2qaCGhPBAMmJCXHbNuSkRNLZZKKwduWmskuObFQ8wkLK/VzkmnL+6o4TJsSEszojm8gUT+TC7gqrGtmH17XBNMxmxIcxICmevBFIuMexASmttAX4AfAjkAC9rrfcP97zDcbi6ibZOmySai1EjwOQrZTrEmLdsygSmxofyxMYjPUaIbDbN5kM1LJsS49LfBU8knBfVDS6QSo4MIjLY76SE88KaZr4qPMZlp05EKcWVp03CYtO8+FVxH2fqX2FtM2kTQpgzMZLssgaXrQYcz1xSR0pr/Z7WeqrWerLW+l5XnHM4JNFcCCG8j1KKtcvSOVDe+P/t3Xl0lfWdx/H3994kZN8IYcnCDbLJkoAGKOAGosW9rdZij621i2Nrx9aptVXPmY4zbefM6WY7U9t6bGs7am3rhrQ6LYt1QUV2EMISCTtkIUBCQpab/OaPe4MJZL1Z7iX5vM7xSJ7nuc/zO+eruV9+v+/z/fHvf9lOg7/5zLmio1Ucr21kfh/0j2ptQmYS8THeAa2TOlAZ2K2gu8XmZhbocN5qRuqFDQfxGHxiZjYAvowELps4gmfW7Mff1NzRrTpV72/i4PHT5GUkMD0rhdqGJva0qpmS0AzKzuYejzEtK1mbv4qIRJhbLs7mc/N8/Hb1Xj71+DtntkhaXRzsH9WH9VEAXo8xLSulX97ca2p27bYQ2F9ZS2y0hxGJ3d9VY2pWMjuPVtPgb6a52fH8hkPMH5/BqJTYM9d85iNjOVpVx4oedIlvM65jtTgH40YknNlCR8t7vRcV7gH0hxsLxnBjwZhwD0NERM4S5fXwbzdOZZYvnW89v4XrfvYmP7l1BquLjzE+M5GRybFd36SHZuSk8uTbe2nwNxMTFdr8wdJNh/jl63uoqfdT2+DnVL2fusZmctLjePauuWS1arzZ8sZeT5Yop41JoaGpmd1l1ZysbeTQidM8sHhSm2sWTs4kKzWO/313H4unjW5zbtvhk3z/lSK+umDCmc2iz9bS+iAvI4FxIxKJj/Gy5eAJbr44u9vjlHMNyhkpERGJbNflj2bZP1/C6JQ47nxyLW8VVzC/gwSgtwqyU2nwN7PzaHXI9/jV63s4XtPAzNxUrp46is/O9XHvwvGcqGnkC0+ubbNX3v7K2h633mkpRdl2qIrnNhwkaVgUH506qs01Xo/x6Tm5rC4+RnFZYEnOOcfv39nLx3/+NquLj/HSxkMdPmNvMJHyZSScmanbog2Te02JlIiIhEVeRgIvfmUet83OpanZceWFI/vlOQU5gWWsTSEu7x05eZrtR6q4c76Pny6Zyfc/Pp2Hrr2Qf7l6Er+4/WKKy05xzzMb8Tc145zj4PHT3S40b+EbnkBCjJc1JZW8uvUo1xeMbnfT5lsLc4j2Gk+v2cfJ0418+akN/OvSbcwbP5yLclM7XcIsqaghIzGG5NhoAPKzUth+uIrGEGuuJECJlIiIhE1stJf//MR01j68iMsm9k+z5qzUODISY0J+c2/VjjIArrww85xzl0zI4Lsfm8Ybu8r5zsvbOF7byKl6f48TKY/HmDomhZc2HeJ0YxM3X9T+ctuIpGFcM200z607yHU/e5MVRaU8dO1kfnPHLOaPz2B3O409W+ypqCGvVWuJ6dkp1Pub2VUa+kydKJESEZEIMCKp+4XZPWVmFGSnhp5IFZWRmx7f4V6YS2bncvflF/D0mv08sizQ/ScnrXtv7LU2NSuZpmaHb3g8F4/tuEHvZ+aOpbrej3Pwp7vnctdlF+DxGPnZqTQ1uw43hy45K5HKzw60hlBjzt5RIiUiIoNeQU4qxeWn2tQydUddYxOrP6hg4eTMTovHH/joJK6dPoqlmwIbe+QO7/n2ZC29D2++KLvTZ83ypfPMl+bwyr2XclHuhwlXQfBNvM3tJEbVdY2UV9fja5VI+YbHkxQbpTqpXlIiJSIig15BTirOtZ19qan3815J5ZkWDO1554Nj1DU2s3Dyuct6rXk8xo9vncGMnFS8Huv2PnutLZycycdmjOG2ObldXjvvggxS4qPbHMtMjmVUcmy7e+jtC3Z2b9013szIz07RjFQvDcr2ByIiIq21zNb87p29vLz5MJsOnGBXaTXNwb5Ky++7HG87e7Ou3FFKfIyXOePSu3xGbLSX339hNrtLq0kY1vOv1/SEGB5dMrPHn2stPzul3d5QH7Y+aLs8OT0rlV+/tYd6fxPDos4tbpeuaUZKREQGvdT4GCaOTORv20p59f2jZCbH8tWFE7h34Xj2lNfwt21Hz/mMc45VRWVcOiGj20lGcmw0F4/tOunqLwU5qZRU1HDydNslzJLyGsxg7FlLjvnZKTQ2OXYcUcF5qDQjJSIiQ8JTX5xDTX0TvuEfNstsanYs23KEx/5RzDXTRrWpTdpxtJrDJ+v42qIJ4Rpyj7V0LN968CSXTPiwS3xJxSnGpMSd01LhTIfzQyfP7EsoPaMZKRERGRIyk2LJy0hokyx5Pcbdl4/j/UNVvLG7os31LW0PFkzqvD4qkuRnBTdpPqtOquRYbZs39lpkpcaRnhDD1n7YQmeoUCIlIiJD2sdnZjM6JZbHXituc3zVjjLys1PI7Idta/pLSnw0eRkJbVo9OOcoKT/VbiJlZkzPar+uSrpHiZSIiAxpMVEevnjpONaUVLJ+XyUAlTUNbNh/vMu39SLR2QXnlTUNVNX5202kIFCIv6u0usNGntI5JVIiIjLk3TY7h7T4aB577QMA/rGzDOc4TxOpVI5W1VFWVQcEGnECHSZS07NTaXaw/YhmpUKhREpERIa8+Jgo7pyfx8odZRQdqWLljjJGJA1jWrBJ5vnk7Mace7pIpM4UnGt5LyRKpERERIA75vpIiPHy36t288bOchZOysTTTm+pSDd1TApej51pzLm3ooYoj5HdwbY1I5NjyUwaxuriinbPS+eUSImIiBAo1L597lhe2XqU6no/C9vZpPh8EBfjZUJm4pkZqZKKGnKHxxPl7fgr/7bZuawoKmNlUelADXPQUCIlIiIS9IVL8oiJ8hDj9XDJ+IyuPxChCrJT2XLwROCNvYoa8oa3v6zX4p4F45k8KomHXtx6TjNP6ZwSKRERkaDMpFjuWzSRO+f7QtrmJVLk56RworaR/ZW1gUSqg/qoFjFRHn5wSwEVpxr47l+2D9AoB4fz978SERGRfvDlKy4I9xB6rSA70Jjzb9uOUu9vJm9E54kUwPTsFP7psnE89o8PuC5/NFecR41Iw0kzUiIiIoPMpFFJxER5eGnjYaDjN/bOdu+VExifmciDL2yluk5LfN2hREpERGSQifZ6mDI6me1HqoDuJ1Kx0V5+cEs+pVV1fP+VHf05xEGjV4mUmf3AzHaY2RYze9HMtOOhiIhIBGjpJxUX7WVkUve3uZmZm8aXLh3HH97bz1u71RKhK72dkVoOTHPO5QO7gAd7PyQRERHprYKcwNyGLyOhx/2w7rtqIr7h8fx4+c7+GNqg0qtEyjn3d+ecP/jju0B274ckIiIivZUfLDgf181lvdZio70snjaarYdOUtfYN3vwLd10iMWPvsE3/7yZP609wJ7yUzjn+uTe4dSXNVKfB17t6KSZ3WVm68xsXXl5eR8+VkRERM42LiOBnPQ4Lh6bFtLnZ/nSaGxybD5wotdj2bj/ON/88xZqG5pYUVTKA89vYeGPXmfW91Zw3x830eBv7vE9G/zNPLJsG7tLq3s9vt7osv2Bma0ARrVz6mHn3NLgNQ8DfuDpju7jnHsceBygsLDw/E9BRUREIpjHY7x+/4KQt7lpScDW7TvOnHHDQx5HWVUddz+1npEpw1h6z3xS46P5oLyGtXsrWVlUxosbD7FkVk6Pn/HGrnJ+u3ovl00YwYSRSSGPr7e6TKScc4s6O29mdwDXA1e6wTBHJyIiMkj0Zq/A1PgYxmcmsm5vZcj3qPc3cfdT66k67eeFr8wjLSEGgPGZiYzPTGTx1FHM/I/lrN1b2eNEatmWw6TGR3PJhPB2oO/tW3uLgW8BNzrnavtmSCIiIhIJZvnSWL/vOM3NPZ8ncc7xnaXb2LD/BD/8ZAEXjk4+55q0hBgmjkzkvb3He3Tv0w1NLN9eyjXTRhPdyR6CA6G3T/8fIAlYbmabzOyXfTAmERERiQAXj02nqs5PcfmpHn/2qTX7eXbtAe5ZcAHX5Y/u8LpZvnQ27DtOUw+StVU7yqhtaOKGgo7vO1B6+9beeOdcjnNuRvCfu/tqYCIiIhJehcE6qbU9XN5bv6+SR17exsLJmXzjqkmdXjs7L51T9X6Kgs1Du2PZ5sOMSBrGnLzQa7f6ijqbi4iISLvGDo8nIzGG9T1cenvizRJS42N4dMmMLuu0ZvnSge4na9V1jazaWcZ100fj7UUNWF9RIiUiIiLtMjMKx6azbl/3E6l6fxNv7CrnqikjSY6N7vL6MalxZKXGdTuRWr69lAZ/MzcUjOn2mPqTEikRERHpUKEvjf2VtZRV1XXr+jV7KqlpaOKqKZndfsYsXxrvlRzvVoPOZZsPk5Uax0W5kbErnRIpERER6VDrflLdsaKolNhoD/Mu6H5bgll56VScqmffsc4bAByvaeDN3RXcUDAGs/Av64ESKREREenE1DEpxEZ7WNeNOinnHCuLyrh0wghio73dfsbsYJ3Ue10s7736/lH8zS4i3tZroURKREREOhQT5aEgO5X1+7quYSo6Us2hE6dZdGH3l/Ug0KAzLT6atSWdP2PZ5sOMG5HAlHZ6UoWLEikRERHpVKEvjfcPV1Hb4O/0upVFpQAsmNyzRMrMuHhseqcF52VVdbxbcowb8iNnWQ+USImIiEgXCn3pNDU7NnWxgfGKolJm5KSSmRTb42fMzktj77FayqrbL2r/69YjOEdELeuBEikRERHpwkW5aZjRaT+psqo6Nh882eNlvRZn+kmVtP+MZZsPc+HoZMZnhm+D4vYokRIREZFOpcRFMzEzibWdvLm3akcZAIumjAzpGdOyUoiL9ra7vFdcdooN+09E3GwUKJESERGRbij0pbGxkz3xVhSVkpUax6SRoc0YRXs9zMxNPSeRqm3w89VnNpAaH80tF2WHdO/+pERKREREulToS6O63s+u0upzzp1uaOKt4gqumjKyV4Xghb50io5UUV3XCATaKTz4wlZ2llbzsyUzyUzuee1Vf1MiJSIiIl0qHBuoYWqvMefq4grqGpu5MsT6qBazfek0O1gffMaTb+9l6abD3H/1JC6bOKJX9+4vSqRERESkS9lpcYxMHsa7Hxw7ZyuXlTtKSRwWxZy84b16xszcVLweY+3eSt4rqeR7fy3iqikj+fLlF/Tqvv1JiZSIiIh0ycxYMCmTv249wqd+9S5vF1fgnKO5OdDN/PKJI4iJ6l1akTAsimljkllZVMZXnt5Abno8P7q1AI8ncvpGnS0q3AMQERGR88MjN01lyphkfv5aMZ9+Yg2z89K5ZtooyqrrWdSDTYo7M8uXzhNvlRAf4+WZL80hOTa6T+7bXzQjJSIiIt0yLMrLZ+f6eP2bC/i3G6awt6KGR5Ztx2NwxcS+SaQunTgCM/ivm/OZGOIbgAPJzl7nHAiFhYVu3bp1A/5cERER6Tt1jU38ce0BnHN8bn5en9zTOUdlTQPDE4f1yf36gpmtd84VtndOS3siIiISkthoL3fM8/XpPc0sopKormhpT0RERCRESqREREREQqRESkRERCRESqREREREQtQniZSZ3W9mzswy+uJ+IiIiIueDXidSZpYDXAXs7/1wRERERM4ffTEj9RPgAWDgG1KJiIiIhFGvEikzuxE45Jzb3I1r7zKzdWa2rry8vDePFREREYkIXXY2N7MVwKh2Tj0MPARc7Zw7aWZ7gULnXEWXDzUrB/b1fLg9kgF0ORYZcIpL5FFMIpPiEnkUk8g0EHEZ65wb0d6JkLeIMbPpwEqgNngoGzgMzHbOHQ3ppn3IzNZ11M5dwkdxiTyKSWRSXCKPYhKZwh2XkLeIcc5tBc7sUNiTGSkRERGRwUB9pERERERC1GebFjvnfH11rz7yeLgHIO1SXCKPYhKZFJfIo5hEprDGJeQaKREREZGhTkt7IiIiIiFSIiUiIiISokGZSJnZYjPbaWbFZvbtcI9nKDKzHDN7zcyKzGybmX0teDzdzJab2e7gv9PCPdahxsy8ZrbRzP4S/FkxCTMzSzWz58xsR/D/mbmKS3iZ2X3B313vm9kfzCxWMRl4ZvYbMyszs/dbHeswDmb2YPC7f6eZfXQgxjjoEikz8wI/B64BpgC3mdmU8I5qSPID33DOXQh8BLgnGIdvAyudcxMI9CFTojvwvgYUtfpZMQm/nwL/55ybDBQQiI/iEiZmlgXcS6ClzzTACyxBMQmHJ4HFZx1rNw7B75glwNTgZx4L5gT9atAlUsBsoNg5t8c51wA8C9wU5jENOc65I865DcE/VxP4YsgiEIvfBS/7HfCx8IxwaDKzbOA64IlWhxWTMDKzZOAy4NcAzrkG59wJFJdwiwLizCwKiCfQcFoxGWDOuTeAyrMOdxSHm4BnnXP1zrkSoJhATtCvBmMilQUcaPXzweAxCRMz8wEzgTXASOfcEQgkW7Rq6ioD4lECm4w3tzqmmITXOKAc+G1wyfUJM0tAcQkb59wh4IfAfuAIcNI593cUk0jRURzC8v0/GBMpa+eYejyEiZklAs8DX3fOVYV7PEOZmV0PlDnn1od7LNJGFHAR8Avn3EygBi0ZhVWw5uYmIA8YAySY2e3hHZV0Q1i+/wdjInUQyGn1c8segDLAzCyaQBL1tHPuheDhUjMbHTw/GigL1/iGoPnAjcHtnJ4FFprZUygm4XYQOOicWxP8+TkCiZXiEj6LgBLnXLlzrhF4AZiHYhIpOopDWL7/B2MitRaYYGZ5ZhZDoPDs5TCPacgxMyNQ81HknPtxq1MvA3cE/3wHsHSgxzZUOecedM5lB3chWAKscs7djmISVsFN3g+Y2aTgoSuB7Sgu4bQf+IiZxQd/l11JoM5TMYkMHcXhZWCJmQ0zszxgAvBefw9mUHY2N7NrCdSCeIHfOOe+F+YhDTlmdgnwJrCVD+txHiJQJ/UnIJfAL6tPOufOLiSUfmZmVwD3O+euN7PhKCZhZWYzCLwAEAPsAe4k8BddxSVMzOwR4FME3kDeCHwRSEQxGVBm9gfgCiADKAW+A7xEB3Ews4eBzxOI29edc6/2+xgHYyIlIiIiMhAG49KeiIiIyIBQIiUiIiISIiVSIiIiIiFSIiUiIiISIiVSIiIiIiFSIiUiIiISIiVSIiIiIiH6fxsiLJFWT1ojAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ar_1_process_unit_root = generate_ar_process(1, [1], 100)\n",
    "plt.figure(figsize=(10,4))\n",
    "plt.plot(ar_1_process_unit_root)\n",
    "plt.title('Non-Stationary AR(1) Process', fontsize=18)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ADF Statistic: -1.224748\n",
      "p-value: 0.662860\n"
     ]
    }
   ],
   "source": [
    "perform_adf_test(ar_1_process_unit_root)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# AR(2) Process"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Stationary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Stationary AR(2) Process')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ar_2_process = generate_ar_process(2, [.5, .3], 100)\n",
    "plt.figure(figsize=(10,4))\n",
    "plt.plot(ar_2_process)\n",
    "plt.title('Stationary AR(2) Process', fontsize=18)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ADF Statistic: -5.771185\n",
      "p-value: 0.000001\n"
     ]
    }
   ],
   "source": [
    "perform_adf_test(ar_2_process)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Non-Stationary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Non-Stationary AR(2) Process')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ar_2_process_unit_root = generate_ar_process(2, [.7, .3], 100)\n",
    "plt.figure(figsize=(10,4))\n",
    "plt.plot(ar_2_process_unit_root)\n",
    "plt.title('Non-Stationary AR(2) Process', fontsize=18)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ADF Statistic: -1.530086\n",
      "p-value: 0.518579\n"
     ]
    }
   ],
   "source": [
    "perform_adf_test(ar_2_process_unit_root)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
